The author studies the well-posedness problem for a model of absorption and diffusion in ultranapkins, consisting of cellulose with granules of a super-absorbent. The mathematical model consists in an evolutionary problem for concentrations of fluids u in the cellulose v in the granules, respectively. The fluid is transported in the cellulose but not in the granules. Therefore, u, v satisfy a nonlinear diffusion equation u, coupled with an ordinary differential equation. Moreover, since the fluid can penetrate the napkin only through a part of its boundary, the problem involves discontinuities on the boundary. Employing comparison principles the author proves the existence and uniqueness of regular solutions in a three-dimensional bounded domain which do not exceed the saturation concentration u1, v1.
Study of the mathematical model for absorption and diffusion in ultra-napkins
MANNUCCI, PAOLA
1995
Abstract
The author studies the well-posedness problem for a model of absorption and diffusion in ultranapkins, consisting of cellulose with granules of a super-absorbent. The mathematical model consists in an evolutionary problem for concentrations of fluids u in the cellulose v in the granules, respectively. The fluid is transported in the cellulose but not in the granules. Therefore, u, v satisfy a nonlinear diffusion equation u, coupled with an ordinary differential equation. Moreover, since the fluid can penetrate the napkin only through a part of its boundary, the problem involves discontinuities on the boundary. Employing comparison principles the author proves the existence and uniqueness of regular solutions in a three-dimensional bounded domain which do not exceed the saturation concentration u1, v1.Pubblicazioni consigliate
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